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# A certain company that sells only cars and trucks reported t

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Math Expert
Joined: 02 Sep 2009
Posts: 51223
A certain company that sells only cars and trucks reported t  [#permalink]

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11 Mar 2014, 23:04
3
23
00:00

Difficulty:

45% (medium)

Question Stats:

74% (02:31) correct 26% (03:10) wrong based on 712 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?

(A) 1:2
(B) 4:5
(C) 1:1
(D) 3:2
(E) 5:3

Problem Solving
Question: 155
Category: Algebra; Arithmetic First-degree equations; Percents
Page: 82
Difficulty: 600

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A certain company that sells only cars and trucks reported that  [#permalink]

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12 Mar 2014, 22:07
7
1
getzgetzu wrote:
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

A. 1 : 2
B. 4 : 5
C. 1 : 1
D. 3 : 2
E. 5 : 3

This is a weighted average question. Average of -11% and +7% is +1%.
Using w1/w2 = (A2 - Aavg)/(Aavg - A1),
we get w1/w2 = (7 - 1)/(1- (-11)) = 6/12
Revenue from Car:Revenue from Trucks = 1:2

For explanation of the formula and other details, go to:
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... ge-brutes/

For another discussion on the same question, check: a-certain-company-that-sells-only-cars-and-trucks-reported-73058.html#p541483
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Math Expert
Joined: 02 Sep 2009
Posts: 51223
Re: A certain company that sells only cars and trucks reported t  [#permalink]

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11 Mar 2014, 23:04
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SOLUTION

A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?

(A) 1:2
(B) 4:5
(C) 1:1
(D) 3:2
(E) 5:3

Let the revenue from cars in 1996 be $$c$$ and revenue from trucks in 1996 be $$t$$.

Total revenue in 1997 would be $$0.89c+1.07t$$.
Also as total revenue in 1997 were up 1 percent from 1996, then total revenue in 1997 would be $$1.01(c+t)$$.

Equate above two: $$0.89c+1.07t=1.01(c+t)$$ --> $$\frac{c}{t}=\frac{1}{2}$$.

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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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12 Mar 2014, 18:43
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Attachments

car.jpg [ 29.32 KiB | Viewed 8056 times ]

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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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12 Mar 2014, 19:15
1
The company sells only cars and trucks.
Let c = revenue from car sales in 1996
Let t = revenue from truck sales in 1996
Equating the total revenue in 1997 with the individual revenue from selling cars and trucks in 1997,
c(0.89) + t(1.07) = (c+t) (1.01)
Dividing throughout by t,
(c/t) (0.89) + 1.07 = (c/t + 1) (1.01)
=> (c/t) (0.12) = 0.06
=> (c/t) = 1/2

Option (A).
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Joined: 03 Aug 2012
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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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15 Mar 2014, 19:49
1
This is how my brain processed this one,

Step 1 --> Set up the equations.

In 1996: R = C+T
In 1997: 1.01R = .89C+1.07T

Remember we are looking for C/T.

Step 2 --> Substitute

1.01(C+T) = .89C+1.07T or,
1.01C + 1.01T = .89C+1.07T

Step 3 --> Solve

.12C = .06T
.12C/T = .06
C/T = .06/.12
C/T = 1/2 or 1:2

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Re: A certain company that sells only cars and trucks reported t  [#permalink]

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20 May 2014, 12:26
3
1
Car-------------------------------Truck
(-11%)-----------------------------(+7%)
-------------------------(+1%)-------- (Wtd Avg)
--------(12%)------------/----(6%)--
Thus ratio of Car Sales/Truck Sales = 6/12= 1/2

FWIW, this is one of the fastest and easiest way to solve such problems
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Joined: 22 Sep 2016
Posts: 2
Re: A certain company that sells only cars and trucks reported t  [#permalink]

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15 Dec 2016, 21:55
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?

(A) 1:2
(B) 4:5
(C) 1:1
(D) 3:2
(E) 5:3
Attachments

Screen Shot 2016-12-16 at 1.50.41 PM.png [ 340.19 KiB | Viewed 3760 times ]

Manager
Joined: 31 Dec 2016
Posts: 73
Re: A certain company that sells only cars and trucks reported t  [#permalink]

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29 Jul 2017, 20:05
Here is a simpler solution
X=Cars
Y= Trucks.

Obviously intuitively for sales to grow Y would need to be bigger than X as X was negative and Sales overall were positive.
Attachments

car problem.png [ 269.89 KiB | Viewed 2633 times ]

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Joined: 09 Sep 2013
Posts: 9183
Re: A certain company that sells only cars and trucks reported t  [#permalink]

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12 Aug 2018, 19:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A certain company that sells only cars and trucks reported t &nbs [#permalink] 12 Aug 2018, 19:02
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